Question

Will fan and medal!!

Answer 1

Using the following equation, find the center and radius of the circle. You must show all work and calculations to receive credit.
x2 + 2x + y2 + 4y = 20

Answer 2

\[x^2+2x+y^2+4y=20\]

Answer 3

@welshfella

Answer 4

I know I have to complete the square but I have no clue how to do it.

Answer 5

convert it to the form
(x - a)^2 + (y - b)^2 = r^2


complete the square x^2 + 2x and y^2 + 4y

Answer 6

We use (h-k)^2+(y-k)^2=r^2 but it's the same thing as the form you gave me.

Answer 7

x^2 + 2x + y^2 + 4y = 20
(x + 1)^2 - 1 + (y + 2)^2 - 4 = 20


to complete the square you take half of the coefficient of x then you have to subtract this value squared

(x + 1)^2 = x^2 + 2x + 1 - so you have to subtract 1^2 from this to make x^2 + 2x

Answer 8

(x + 1)^2 + (y + 2)^2 = 20+1 + 4 = 25

so if you compare this with the general equation
you'll see that center = (-1,-2) and radius = sqrt25 = 5

Answer 9

Thank you so much. I have one more question if you dont mind?

Answer 10

well i must go in 10 minutes so we'll see how much i can do in that time

Answer 11

Prove that the two circles shown below are similar.

Answer 12

I know that all circles are similar, but how do I prove it?

Answer 13

oh must go now I'm sure jhannybean can help

Answer 14

Okay thank you!

Answer 15

\[x^2 + 2x + y^2 + 4y = 20\]\[(x^2+2x) + (y^2+4y)=20\]\[(x^2+2x+\color{red}{1}) +(y^2+4y+\color{red}{4})=20+\color{red}{1}+\color{red}{4}\]\[(x+1)^2+(y+2)^2=25~~~\checkmark \]

Answer 16

Haha you dont have to @welshfella

Answer 17

@Jhannybean Could you help with the circle question? It's my last one. :/

Answer 18

hint: try creating triangles within the circles and then using their ratios in comparison.

Answer 19

So once i have the ratios what do i do?

Answer 20

If we compare al the sides in a ratio, we would see it has a proportional relationship

Answer 21

First find the hypotenuse of both triangles, the smaller triangle having a hypotenuse of x. and the bigger one having hypotenuse of y. \[c_1 : x^2= 2^2+2^2 = 8 \iff x=\sqrt{8}\]\[c_2 : y^2=5^2+5^2 = 50 \iff y=\sqrt{50}\]

Answer 22

What about dilations? Couldn't we see if they are similar that way?

Answer 23

Then we can say by the SSS theorem, \[\frac{2}{5} = \frac{\sqrt{8}}{\sqrt{50}}\]

Answer 24

Hmm..i'm not really familiar with dilations! sorry.

Answer 25

Okay well thank you!

Answer 26

@cwrw238 could you help me understand dilations? :)

Answer 27

I understand the way you did it, and it makes perfect sense, so no worries. :) thank you for your help!

Answer 28

Oh cool! no problem.